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locus related to a perpendicular line to bases of trapezoid

Source: Sharygin Geometry Olympiad 2016 Final Round problem 3 grade 8

July 22, 2018
geometryLocustrapezoidperpendicular

Problem Statement

A trapezoid ABCDABCD and a line ℓ\ell perpendicular to its bases ADAD and BCBC are given. A point XX moves along ℓ\ell. The perpendiculars from AA to BXBX and from DD to CXCX meet at point YY . Find the locus of YY .
by D.Prokopenko
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